Triple diamond-alpha integral and Hölder-type inequalities. (English) Zbl 1497.26036
Summary: In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26E70 | Real analysis on time scales or measure chains |
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